Newton's Laws and Atwood's Machine

Transcription

1 Newton's Laws and Atwood's Machine Purpose: In this lab we will verify Newton's Second Law of Motion within estimated uncertainty and propose an explanation if verification is not within estimated uncertainty. Equipment: Table Clamp, Long Rod, Right Angle Clamp Smart Pulley Smart Pulley Photogate Hooked Mass Set Thread or Fishing Line Meter Stick Stopwatch Theory: George Atwood was a British fellow who lived in the latter half of the 18 th century. He was educated, and later lectured, at Trinity College Cambridge. While he was a very popular teacher, showing many demonstrations during his lectures, he is best known for his publication A Treatise on the Rectilinear Motion... (1784). In this work he describes a machine that demonstrates the laws of uniformly accelerated motion due to gravity. This machine is now known as Atwood s machine, and has apparently become so ingrained in the pedagogy of Physics that nothing interesting is written about it. The Atwood s machine is the logical extension of the investigation of Newton s Second Law of Motion from the previous two labs. Rather than one mass being supported by a frictionless surface, both masses are allowed to hang from the pulley. There are now two external forces acting parallel to the direction of motion: the force due to gravity on m 1 and the force due to gravity on m 2. A free-body force diagram for each of the masses will include the internal force of rope tension. The derivation of the system s acceleration is left as an exercise, so it will not be shown here. However, if you run into trouble, it may be helpful to go back to the Newton s Second Law lab and look at the derivation of acceleration shown there. 1 of 6

2 Experiment: smart pulley-photogate m 1 LabPro m 2 Figure 1 Basic Experimental Set-Up Part A: Acceleration with No Air Resistance 1. Set up Atwood's machine as shown in sketch. Some of the smart pulley-photogates come as one piece, others you may have to put together yourself. 2. Connect the AC adapter to the LabPro by inserting the round plug on the 6-volt power supply into the side of the interface. Shortly after plugging the power supply into the outlet, the interface will run through a self-test. You will hear a series of beeps and blinking lights (red, yellow, then green) indicating a successful startup. 3. Attach the LabPro to the computer using the USB cable that is Velcro-ed to the side of the computer box (do not unplug the USB cable from the computer!). The LabPro computer connection is located on the right side of the interface. Slide the door on the computer connection to the right and plug the square end of the USB cable into the LabPro USB connection. 4. Connect the Smart Pulley/Photogate to the DIG/SONIC1 port of the LabPro. If you are using a one-piece Smart Pulley/Photogate, a PASCO or very old Vernier Photogate, you will need to use the digital adapter. If you are using a newer Vernier (with removable cable), simply remove the cable with the Phono plug, and connect the Photogate Cable with a British-Telecom plug on one end. 5. You will be using mass-pairs of 20 and 30 grams, 30 and 40 grams, 40 and 50 grams, 50 and 60 grams. Use the balance to determine the actual value of the masses, and record. 6. Measure the height of m 1 above the floor. 7. Release m 2 and use the stopwatch to determine the time for m 1 to fall from its original position to the floor. Calculate the acceleration using the equation h = ½ at 2, where h is the height of m 1 above the floor. 2 of 6

3 8. Open the file atwood.xmbl (or.cmbl) in the Experiments folder on the desktop. This will start the program Logger Pro3.3 and bring up the appropriate data file. If you do not have an auto-id sensor (which is the likely case), a dialog box will pop up asking you to confirm the sensors being used. If you have the suggested sensor attached to the LabPro in the suggested port, click OK. If the OK button is not active, ask your instructor for help. 9. Once Logger Pro 3 is open, click on Experiment > Set Up Sensors > LabPro 1. Click on the photogate icons, and verify that Motion Timing is selected under Current Calibrations. In the same menu, choose Set Distance or Length, make sure that Smart Pulley (10 Spoke) in Groove is selected. The program calculates the acceleration and velocity of the falling mass by treating the pulley as a picket fence with the proper spacing. 10. Now press Collect and release the mass. If the acceleration nearly matches the value you measured in Step 7, proceed to the next step. Repeat this process with another set of masses. 11. For each pair of masses described in Step 5, run the experiment at least three times. Be sure to save at least one run on the hard drive or on disk (in case the computer crashes!). Part B: Acceleration with Air Resistance 1. Repeat Part A with a 3X5 index card taped to the bottom of the falling mass. 2. Discuss the effect that air resistance has on the system s theoretical acceleration. Analysis: 1. For each run, examine the acceleration vs. time graph. Highlight a relatively constant portion (including at least 10 data points), and click on the Statistics button. Record (in your own table) the average acceleration and standard deviation. 2. For each pair of masses, average the acceleration values obtained from the separate trials (average the average values!). Calculate the uncertainty from the half range relationship (a max - a min )/2. 3. Analyze the system using Newton's Second Law. Isolate each mass, sketch free-body diagrams, write down 2 nd law equations for each mass, and derive the theoretical acceleration, a th, for the system: ( m1 m2 ) a th = g ( m1 + m2 ) where m 1 is the mass that is accelerating toward the ground. Be sure to neatly show your work. 4. Calculate the percent difference for each set-up between the observed (experimental) and the calculated (theoretical) values of the accelerations. Identify which values 3 of 6

4 agreed with the theoretical values within the experimental uncertainty, and which did not. 5. State and discuss your results: Were there any trends in the experimental results? Is there any evidence within the data to suggest that the theory be modified to include other aspects of the system (i.e.: what did we leave out?) Results: Write at least one paragraph describing the following: what you expected to learn about the lab (i.e. what was the reason for conducting the experiment?) your results, and what you learned from them Think of at least one other experiment might you perform to verify these results Think of at least one new question or problem that could be answered with the physics you have learned in this laboratory, or be extrapolated from the ideas in this laboratory. 4 of 6

5 Clean-Up: Before you can leave the classroom, you must clean up your equipment, and have your instructor sign below. If you do not turn in this page with your instructor s signature with your lab report, you will receive a 5% point reduction on your lab grade. How you divide clean-up duties between lab members is up to you. Clean-up involves: Completely dismantling the experimental setup Removing tape from anything you put tape on Drying-off any wet equipment Putting away equipment in proper boxes (if applicable) Returning equipment to proper cabinets, or to the cart at the front of the room Throwing away pieces of string, paper, and other detritus (i.e. your water bottles) Shutting down the computer Anything else that needs to be done to return the room to its pristine, pre lab form. I certify that the equipment used by has been cleaned up. (student s name),. (instructor s name) (date) 5 of 6

6 Data Tables mass pair: 20g and 30g no air resistance height of m 1 above the floor, h: Calculation of acceleration: time of m 1 to fall to floor, t: a by hand : run 1 run 2 run 3 run 4 average acceleration, a exp half-range uncertainty acceleration standard deviation Free-body diagrams and derivation of theoretical acceleration, a th : percent difference between experiment and theory: (Please copy this format for all other mass pairs, and for the case of air resistance. You may print out extra copies from your own computer, NOT in 1824!) 6 of 6